Except "reject all" closes the popup. Gotcha!
So you have to first got to "legitimate interest", uncheck all the individual "purposes", because usually there is no "object all". Once you've done that (with "object all" if you're lucky), you then have to go to individual vendors, because objecting to all the purposes does not cover all the vendors. Yeah. Again, if you're lucky there's an "object all", but usually there isn't. So gotta uncheck all those. There's lots. And often there isn't even a good scrollbar indicator to show how far you've gotten. If there is it's just depressing.
Then you can hit "Reject All". And it's not entirely clear if "Reject All" doesn't turn the LIs back on, because, once again, that dismisses the dialog.